A profit-maximizing firm in a competitive market is currently producing 100 units of output. It has average revenue of $10, average total cost of $8, and fixed costs of $200.
a. What is its profit?
b. What is its marginal cost?
c. What is its average variable cost?
d. Is the efficient scale of the firm more than, less than, or exactly 100 units?
a. To calculate the profit of the firm, we need to first find the total revenue and total cost.
Total revenue = Average revenue * Quantity = $10 * 100 = $1000
Total cost = Average total cost * Quantity = $8 * 100 = $800
Profit = Total revenue - Total cost = $1000 - $800 = $200
Therefore, the profit of the firm is $200.
b. The marginal cost of a firm can be found by calculating the change in total cost when output increases by one unit.
Marginal cost = Change in total cost / Change in quantity
In this case, since the firm is producing 100 units, any change in quantity will result in a change in total cost. Therefore, the marginal cost is equal to the average total cost, which is $8.
c. Average variable cost (AVC) represents the cost per unit of variable inputs used to produce a certain level of output. It is calculated by dividing total variable cost by the quantity of output.
Total variable cost = Total cost - Fixed costs = $800 - $200 = $600
Average variable cost = Total variable cost / Quantity = $600 / 100 = $6
Therefore, the average variable cost for this firm is $6.
d. The efficient scale of a firm refers to the output level at which the firm achieves its lowest average total cost. In a competitive market, the efficient scale typically occurs at the output level where the firm has reached its minimum efficient scale (MES).
Based on the given information, we do not have enough information to determine whether the efficient scale of the firm is more than, less than, or exactly 100 units. The information provided only indicates that the firm is currently producing 100 units, but it does not tell us whether this is the most efficient level of production for the firm.
To answer these questions, we need to understand the concepts of profit, marginal cost, average variable cost, and efficient scale.
a. Profit is calculated by subtracting total costs from total revenue. In this case, we have average revenue and average total cost. To find total revenue, we multiply average revenue by the number of units produced. In this case, average revenue is $10 and the firm is producing 100 units, so total revenue is $10 x 100 = $1000. Total cost is the sum of average total cost and fixed costs. In this case, average total cost is $8 and fixed costs are $200, so total cost is $8 x 100 + $200 = $1000. Therefore, the firm's profit is $1000 - $1000 = $0.
b. Marginal cost is the cost of producing one additional unit of output. To find marginal cost, we can look at the change in total cost when output increases by one unit. In this case, since total cost is already given, we can assume that average variable cost is equal to marginal cost. Therefore, the marginal cost is $8.
c. Average variable cost is calculated by dividing the total variable costs by the number of units produced. Total variable costs can be found by subtracting fixed costs from total costs. In this case, fixed costs are $200 and total costs are $8 x 100 + $200 = $1000. Therefore, total variable costs are $1000 - $200 = $800. Since the firm is producing 100 units, the average variable cost is $800 / 100 = $8.
d. The efficient scale of a firm is the quantity at which the average total cost is at its minimum. In this case, the average total cost is $8. However, we cannot determine the efficient scale based on this information alone. We would need more data to analyze the relationship between quantity produced and average total cost in order to determine whether the efficient scale is more than, less than, or exactly 100 units.